Advil that has a half life of 4 hours. What this means is that after this
time there is only half of the amount of Advil left in a sample is half of
its original amount.
a) If the original sample size was 200 milligrams, write an equation using the half
life formula that will represent the M, of the Advil material in milligrams that
remains after âtâ days. (2 marks)
b) Use this equation to determine exactly how long it takes for the same to decay
to 50 milligrams. Show your workings in detail using the equation.
If you were to take 200 milligrams of Advil how many milligrams will remain in the
body 10 hours later? Answer to two decimal places. Show your workings in
detail using the equation
Without the log function
a) The half life formula for the decay of Advil is: M = M0 * (1/2)^(t/4), where M0 is the original sample size, M is the amount remaining after time t, and t is the time in hours.
So, if the original sample size M0 is 200 milligrams, the equation would be: M = 200 * (1/2)^(t/4)
b) To determine how long it takes for the sample to decay to 50 milligrams, we can set M = 50 and solve for t:
50 = 200 * (1/2)^(t/4)
(1/2)^(t/4) = 50/200
(1/2)^(t/4) = 1/4
t/4 = log(1/4) / log(1/2)
t/4 = log(1/4) / log(1/2)
t/4 = -2
t = -8
So, it takes 8 hours for the sample to decay to 50 milligrams.
c) To find out how many milligrams will remain in the body 10 hours later, we can substitute t = 10 into the equation:
M = 200 * (1/2)^(10/4)
M = 200 * (1/2)^2.5
M = 200 * 0.1768
M = 35.36
So, approximately 35.36 milligrams will remain in the body 10 hours later.